dr.ing. nagy gyÖrgy tamás 2 (rc an… · dr.ing.nagy‐györgy t. faculty of civil engineering .4...

Reinforced Concrete II. / Beton Armat II.

Dr.ing. NAGY‐GYÖRGY TamásProfessor

E‐mail: tamas.nagy‐gyorgy@upt.ro 

Tel:+40 256 403 935

Web:http://www.ct.upt.ro/users/TamasNagyGyorgy/index.htm 

Office:A219

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.  

Reinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   2

1. INTRODUCTION

2. HISTORY OF THE STM

3. REGIONS IN THE STRUCTURAL ELEMENTS

4. SAMPLES OF DISCONTINUITIES

5. DESIGN OF B & D REGIONS

6. STM EXAMPLES

1. Introduction / IntroducereReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   3

INTRODUCTION

Two design methods for concrete

Conventional design:‐ Determine moment diagram‐ Specify steel in areas of tension

Strut and tie models:‐ Define internal forces in tension and compression (ties and struts)‐ Specify steel in areas of tension

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   4

‐ The Strut‐and‐Tie is an approach which considers all load effects (M, N, V, T) simultaneously

‐ The Strut‐and‐Tie Model (STM) approach is a useful design method forconcrete structures with shear critical elements or disturbed regions

‐ The STM provides appropriate and simplified truss models to representscomplex structural phenomenon

‐ Based on the existing techniques and rules, for a given situation several STM could be developed (is no unique STM!)

‐ The form of a STM depends on the element geometry, by the applied loadsand their position and by the static scheme, conceived in a such way to respect all the specific rules related to the struts, ties and joints

1. Introduction / IntroducereReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   5

1. INTRODUCTION

2. HISTORY OF THE STM

3. REGIONS IN THE STRUCTURAL ELEMENTS

4. SAMPLES OF DISCONTINUITIES

5. DESIGN OF B & D REGIONS

6. STM EXAMPLES

Reinforced Concrete II. / Beton Armat II.

2. History of the STM / Istoria procedeului modelului de bare 

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   6

History of the STM

Walter Ritter (1899) SwitzerlandEmil Mörsch (1902) Germany

Collins & Mitchell (1980) Canada A design method for shear and torsion for regions of a structure whereBernoulli’s hypothesis is applicable

Schlaich et al (1987, 1991) Germany STM based on experimental data, rule of thumb (a broadly accurate guide or

principle, based on practice rather than theory) and past design experiences, based onphysical models which are more understandable flexibility to the designers to reach cheapest or safest solutions

Collins and Mitchell (1991)MacGregor (1992)

Truss analogy was first introduced

Reinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   7

STM was introduced in codes:

AASHTO (1994) American Association of State Highway and Transportation Officials 

ACI 318‐02American Concrete Institute

EC2 ‐ 2004Eurocode 2

2. History of the STM / Istoria procedeului modelului de bare Reinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   8

1. INTRODUCTION

2. HISTORY OF THE STM

3. REGIONS IN THE STRUCTURAL ELEMENTS

4. SAMPLES OF DISCONTINUITIES

5. DESIGN OF B & D REGIONS

6. STM EXAMPLES

Reinforced Concrete II. / Beton Armat II.

3. Regions in the structural elements / Zone în elemente structurale

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   9

Parts of a structural element are classified in two regions: 

1) B‐region (is known as Bernoulli or Beam) Regions of a structure where Bernoulli’s hypothesis is applicable plane section remain plane after bending

facilitates the flexural design of reinforced concrete structures byallowing a linear strain distribution for all loading stages, including ultimate flexural capacity

pure bending

n.a. 

Reinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   10

2) D‐region (from Disturbance or Discontinuity) regions where the beam theory does not apply

bending & shear 

3. Regions in the structural elements / Zone în elemente structuraleReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   11

2) D‐region (from Disturbance or Discontinuity) regions where the beam theory does not apply

occur at regions of geometrical or static discontinuity, such asopenings, changes in cross section or near concentrated loads andreactions.

The strain distributions for this section will not be linear and thelength is usually governed by St. Venant’s principle

3. Regions in the structural elements / Zone în elemente structuraleReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   12

St. Venant's Principle states  “The localized effects caused by any load acting on the body will dissipate or smooth out within regions that are sufficiently away from the location of the load…“

3. Regions in the structural elements / Zone în elemente structuraleReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   13

(Prof. Kovács I., DE)

St. Venant's Principle states  “The localized effects caused by any load acting on the body will dissipate or smooth out within regions that are sufficiently away from the location of the load…“

3. Regions in the structural elements / Zone în elemente structuraleReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   14

Disturbance extends over a length equal to thelargest dimension of the cross section area

(Prof. Clipii T.)

St. Venant's Principle states  “The localized effects caused by any load acting on the body will dissipate or smooth out within regions that are sufficiently away from the location of the load…“

3. Regions in the structural elements / Zone în elemente structuraleReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   15

St. Venant's Principle states  “The localized effects caused by any load acting on the body will dissipate or smooth out within regions that are sufficiently away from the location of the load…“

disturbance no disturbance

(Prof. Clipii T.)

3. Regions in the structural elements / Zone în elemente structuraleReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   16

disturbanceno disturbance

St. Venant's Principle states  “The localized effects caused by any load acting on the body will dissipate or smooth out within regions that are sufficiently away from the location of the load…“

3. Regions in the structural elements / Zone în elemente structuraleReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   17

disturbance no disturbance

St. Venant's Principle states  “The localized effects caused by any load acting on the body will dissipate or smooth out within regions that are sufficiently away from the location of the load…“

(Prof. Clipii T.)

3. Regions in the structural elements / Zone în elemente structuraleReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   18

1. INTRODUCTION

2. HISTORY OF THE STM

3. REGIONS IN THE STRUCTURAL ELEMENTS

4. SAMPLES OF DISCONTINUITIES

5. DESIGN OF B & D REGIONS

6. STM EXAMPLES

Reinforced Concrete II. / Beton Armat II.

4. Samples  of  discontinuities / Exemple de discontinuitățiReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   19

SAMPLES  OF  DISCONTINUITIES ‐ GEOMETRIC DISCONTINUITIES

1. Cross section modification  dapped‐end

(Prof. Clipii T.)

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   20

SAMPLES  OF  DISCONTINUITIES ‐ GEOMETRIC DISCONTINUITIES

1. Cross section modification  dapped‐end

(Prof. Clipii T.)

4. Samples  of  discontinuities / Exemple de discontinuitățiReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   21

SAMPLES  OF  DISCONTINUITIES ‐ GEOMETRIC DISCONTINUITIES

2. Opening  in the web building services

D

4. Samples  of  discontinuities / Exemple de discontinuitățiReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   22

SAMPLES  OF  DISCONTINUITIES ‐ GEOMETRIC DISCONTINUITIES

3. Structural joints, intersections cantilevers, frame joints

(Prof. Kovács I., DE)

4. Samples  of  discontinuities / Exemple de discontinuitățiReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   23

SAMPLES  OF  DISCONTINUITIES ‐ STATIC DISCONTINUITIES

1. Concentrate loads

(Prof. Kovács I., DE)

4. Samples  of  discontinuities / Exemple de discontinuitățiReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   24

SAMPLES  OF  DISCONTINUITIES ‐ STATIC DISCONTINUITIES

2. Support zones

(Prof. Kovács I., DE)

D D D

4. Samples  of  discontinuities / Exemple de discontinuitățiReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   25

SAMPLES  OF  DISCONTINUITIES ‐ STATIC DISCONTINUITIES

3. Prestressing‐end zone

(Prof. Kovács I., DE)

4. Samples  of  discontinuities / Exemple de discontinuitățiReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   26

SAMPLES  OF  DISCONTINUITIES ‐ STATIC DISCONTINUITIES

4. Deep beams

Deep beam

D element

(Prof. Clipii T.)

4. Samples  of  discontinuities / Exemple de discontinuitățiReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   27

SAMPLES  OF  DISCONTINUITIES ‐ STATIC and GEOMETRIC DISCONTINUITIES

4. Samples  of  discontinuities / Exemple de discontinuitățiReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   28

D‐REGIONS

(Prof. Kovács I., DE)

4. Samples  of  discontinuities / Exemple de discontinuitățiReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   29

D‐REGIONS

4. Samples  of  discontinuities / Exemple de discontinuitățiReinforced Concrete II. / Beton Armat II.

Reinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   30

1. INTRODUCTION

2. HISTORY OF THE STM

3. REGIONS IN THE STRUCTURAL ELEMENTS

4. SAMPLES OF DISCONTINUITIES

5. DESIGN OF B & D REGIONS

6. STM EXAMPLES

5. Design of B & D Regions / Calculul zonelor B și DReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   31

Design of B & D Regions

‐ The design of B (Bernoulli or Beam) region is well understood and the entire flexural behavior can be predicted by simple calculation

‐ Even for the most recurrent cases of D (Disturbed or Discontinuity)regions (such as deep beams or corbels), engineers' ability to predictcapacity is either poor (empirical) or requires substantial computationeffort (finite element analysis) to reach an accurate estimation ofcapacity!!!

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   32

D – region is safe if:

‐ the greatest compressive stress on the bearing support is < 0,6fcd

‐ all tensile forces are resisted by reinforcement

‐ sufficient development lengths are provided for the reinforcement

(Prof. Clipii T.)

5. Design of B & D Regions / Calculul zonelor B și DReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   33

STM in Eurocode 2  provides very little guidance in using STM, which covers mainly the effectiveconcrete strength provisions for the various strut‐and‐tie elements.

provides guidance for establishing the effective concrete strength values to use in the struts and nodes for a specific internal force condition and arrangement

5. Design of B & D Regions / Calculul zonelor B și DReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   34

BOTTLE NECK – important Transversal Tensile Forces FAN – negligible TTF PRISM – no TTF

cdRd fmax,

cdRd f 6,0max,

5. Design of B & D Regions / Calculul zonelor B și DReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   35

5. Design of B & D Regions / Calculul zonelor B și DReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   36

5. Design of B & D Regions / Calculul zonelor B și DReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   37

Design recommendations using EC 2 STM provisions

accurate shear strength predictions will achieve  consistent results for beams with a clear shear span to depth ratio of less than 2.  the maximum strains in the tensile reinforcement can be assumed to be strains at 

the point of yielding.

Adequate anchorage should also be provided for the tensile steel reinforcement at the supports to prevent premature reinforcement slip failure. 

If design is to be made purely on EC2 STM provisions, it should be done for beams that have a clear shear span to depth ratio  / of less than 1, which are considered as deep beams. This is to avoid any unsafe predictions in the shear strength. 

For 1 ≤  / ≤ 2, the effective concrete strengths of the direct strut from Modified Compression Field Theory should be used. Anything above the  / range of 2 ought to be designed with the Eurocode 2 Sectional model. 

5. Design of B & D Regions / Calculul zonelor B și DReinforced Concrete II. / Beton Armat II.

Reinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   38

1. INTRODUCTION

2. HISTORY OF THE STM

3. REGIONS IN THE STRUCTURAL ELEMENTS

4. SAMPLES OF DISCONTINUITIES

5. DESIGN OF B & D REGIONS

6. STM EXAMPLES

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   39

CHOOSING  THE  MODEL

(Prof. Clipii T.)

INTUITIVELY

LOAD-PATH METHOD

ELASTIC ANALISYS

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   40

CHOOSING  THE  MODEL

(Prof. Clipii T.)

1. NO MECHANISM

YES !

NO !

3. SHORTER TIES

4. ONE ELEMENT – TWO LOADS – TWO MODEL

2. LESS NUMBER OF TIES

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   41

Simply supported beam subjected to a uniformly distributed load 

blue arrows = compressive stresses black arrows = tensile stresses 

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   42

Simply supported beam subjected to a concentrated load at its center 

Indeterminate Truss  Solving by several iterationblue arrows = compressive stresses black arrows = tensile stresses 

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   43

Simply supported beam subjected to a concentrated load at its center 

Determinate Truss  the member forces to be easily solved

blue arrows = compressive stresses black arrows = tensile stresses 

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   44

Deep Beam with concentrated load

R1 R2

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   45

Deep Beam with concentrated load

R1 R2

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   46

Deep Beam with concentrated load

R1 R2

R1 R2

1 2

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   47

Deep Beam with distributed load

(Prof. Kovács I., DE)

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   48

Bridge Pier Cap Design 

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   49

Bridge Pier Cap Design 

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   50

Bridge Pier Cap Design 

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   51

Bridge Pier Cap Design 

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   52

Bridge Pier Cap Design 

Simple STM

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   53

Bridge Pier Cap Design 

Refined STM

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   54

Bridge Pier Cap Design 

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   55

Bridge Pier Cap Design 

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   56

Dapped‐ends

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   57

Corbels (in conformity to EC2)

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   58

Corbels (in conformity to EC2)

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   59

Beam‐to‐column joints (in conformity to EC2)

6. STM examples / Exemple de modele de bareReinforced Concrete II. / Beton Armat II.

Faculty of Civil Engineering .Dr.ing. Nagy‐György T.   60

Dr.ing. NAGY‐GYÖRGY TamásProfessor

E‐mail: tamas.nagy‐gyorgy@upt.ro 

Tel:+40 256 403 935

Web:http://www.ct.upt.ro/users/TamasNagyGyorgy/index.htm 

Office:A219

THANK YOU FOR YOUR ATTENTION!

Reinforced Concrete II. / Beton Armat II.